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i've looked at it, and i'm not convinced that it does a good job explaining the math the reader doesn't a priori know.

Its one thing to go from mathematical physics to theoretical physics, its another thing to go from pure math with a theoretical computer science bent to mathematical physics and theoretical physics. Does this difference make sense, or am I missing some observation? (i don't know enough to know which is more likely)

You need this: http://mitpress.mit.edu/SICM augmented by e.g. Lanczos Variational Principle (the closest to a platonic ideal of exposition for this didactically elusive topic) and various lecture notes for classical mechanics courses http://www.damtp.cam.ac.uk/user/tong/teaching.html. From there move to Byron & Fuller Mathematical Physics and only then you may question where to next, that's the bare minimum of theory in physics. Baez & Muniain "Gauge Fields & bla bla" has very good narrative on one offer what to do after, Sethna Statistical Mechanics on another. Speaking of bare minimums there's a youtube lecture series by Susskind "Theoretical Minimum of Physics" or sth.

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